A knot with destabilized bridge spheres of arbitrarily high bridge number

Yeonhee Jang; Tsuyoshi Kobayashi; Makoto Ozawa; Kazuto Takao

doi:10.1112/jlms/jdw004

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arXiv · 1501.06263

A knot with destabilized bridge spheres of arbitrarily high bridge number

Yeonhee Jang·Tsuyoshi Kobayashi·Makoto Ozawa·Kazuto Takao

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Abstract

We show that there exists an infinite family of knots, each of which has, for each integer k>=0, a destabilized (2k+5)-bridge sphere. We also show that, for each integer n>=4, there exists a knot with a destabilized 3-bridge sphere and a destabilized n-bridge sphere.

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Yeonhee Jang, Tsuyoshi Kobayashi, Makoto Ozawa, Kazuto Takao. 2016-03-20. A knot with destabilized bridge spheres of arbitrarily high bridge number. https://doi.org/10.1112/jlms%2Fjdw004

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